Proposed physical mechanism that gives rise to cosmic inflation

Early in the Universe a chemical equilibrium exists between photons and electron–positron (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e^{ - } e^{ + }$$\end{document}e-e+) pairs. In the electron Born self-energy (eBse) model the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e^{ - } e^{ + }$$\end{document}e-e+ plasma falls out of equilibrium above a glass transition temperature \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{G} = 1.06 \times 10^{17} K$$\end{document}TG=1.06×1017K determined by the maximum electron/positron number density of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1/(2R_{e} )^{3}$$\end{document}1/(2Re)3 where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{e}$$\end{document}Re is the electron radius. In the glassy phase (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T > T_{G}$$\end{document}T>TG) the Universe undergoes exponential acceleration, characteristic of cosmic inflation, with a constant potential energy density \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi_{G} = 1.9 \times 10^{50} J/m^{3}$$\end{document}ψG=1.9×1050J/m3. At lower temperatures \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T < T_{G}$$\end{document}T<TG photon-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e^{ - } e^{ + }$$\end{document}e-e+ chemical equilibrium is restored and the glassy phase gracefully exits to the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Lambda CDM$$\end{document}ΛCDM cosmological model when the equation of state \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$w = 1/3$$\end{document}w=1/3, corresponding to a cross-over temperature \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{X} = 0.94 \times 10^{17} K$$\end{document}TX=0.94×1017K. In the eBse model the inflaton scalar field is temperature \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T$$\end{document}T where the potential energy density \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi (T)$$\end{document}ψ(T) is a plateau potential, in agreement with Planck collaboration 2013 findings. There are no free parameters that require fine tuning to give cosmic inflation in the eBse model.


Supplementary Material: Interrelationship of eBse model and QED
The CDM  model indicates that the Standard Model for particle physics only describes ~5% of the Universe (the baryons), hence, any model that is capable of describing DE and/or CDM must necessarily be an extension of the Standard Model.A requirement for any extension to the Standard Model is that this new model not conflict with any experimental data that is generally accepted by the scientific community and which is successfully described by the Standard Model.This requirement imposes severe restrictions on the types of extensions to the Standard Model that are possible.The eBse model is an extension of QED, the interaction between photons and electrons.QED forms part of the Standard Model.In QED the electron is assumed to be a point particle possessing zero radius ( 0 e R → ) [1].This point particle assumption, for the electron, leads to various divergences that must be renormalized away, whereby infinite quantities are replaced by finite measurable quantities.In particular, when a (stationary) electron and positron annihilate to give two photons, to conserve energy and momentum, then [2]  Qse is a divergent quantum mechanical self-energy that diverges logarithmically with e R [1] and arises from virtual photons and virtual particles that flit in and out of existence while interacting with the electron or positron.The arrow, in equation (S1), implies that the divergent quantities on the left hand side are replaced by the finite quantity on the right hand side.
A divergent quantity that does not appear explicitly in equation (S1) is the Born selfenergy, corresponding to the energy contained in the electric field that surrounds the electron (or positron).This Born self-energy has the specific form [3,4] where q is the charge and o  is the vacuum permittivity.In QED, to eliminate this divergent quantity, it is assumed that Born e U is subsumed or contained within e m [5].In the 1950s when QED was being developed there was little choice but to make these renormalization assumptions, in order to eliminate diverging quantities, because measurements of the interactions of electrons, positrons, and photons were rather rudimentary at that time.Both Dirac [6] and Feynman [7] expressed reservations about this renormalization process.QED is currently the most accurate theory in physics where, for example, theory and experiment for the electron magnetic moment / B  agree to eleven decimal places [8].The difference between theory and experiment for the electron magnetic moment (in the 12 th decimal place) gives [8] 0.77 12 exp 0.28 ( / ) ( / ) ( / ) 1 10 where 0.77 ( 0.28) represents the error in the theoretical calculation (experimental measurement).
Equation (S3) can be used to estimate an upper bound for the electron radius [9]  The eminent success of QED has meant that few scientists today question the underlying foundations of QED.However, in Physics, there are a number of foundational principles that all physicists agree upon and any discrepancies from these foundational principles potentially point to new physics provided that these discrepancies can be resolved.In particular, Physics must be self-consistent across all subfields, therefore, findings in one subfield may influence the understanding of a different subfield.Additionally, conservation laws, such as the conservation of energy, are expected to hold across all subfields of Physics.
There are two foundational flaws in QED that are not widely recognized: (i) QED is inconsistent with the treatment of ions in soft matter physics.In soft matter physics the solubility of ions in solution is governed by the Born self-energy (equation (S2)) [4].Therefore, to ensure that QED and soft matter physics are self-consistent with each other the Born self-energy, Born e U , cannot be subsumed within e m for an electron.Namely, e m and Born e U must be treated as two separate, independent entities.
(ii) In QED it is assumed that an electron has energy 2 e mc at the point of annihilation with a positron.Additionally, this electron also possesses the same energy as a free particle (at infinite separations).This cannot be correct because, under such circumstances, energy is not conserved.A free electron must possess a greater energy than an electron that is about to be annihilated because work must be done against the Coulomb force in order to separate an electron and a positron from a separation distance of e R out to infinity.
These two foundational flaws in QED can only be resolved if the electron possesses a finite, non-zero radius e R where the Born self-energy Born e U is treated as a separate and distinct quantity from e m .Specifically, if one considers an electron and positron separated by distance r then upon incorporating the Coulomb interaction as well as the Born self-energy, the total energy of interaction between these two particles is [10] which is a justification for the renormalization process in equation (S1).
In the other limit, for free particles, The final issue that requires addressing is "Will the finite electron radius, used in the eBse model, perturb the agreement between theory and experiment in QED? [12,13] , whose value was derived from electron-positron collisions [11,14].For this value of () Upper In summary, the eBse model ensures that (a) the non-local energy is conserved for the electron, (b) the solubility of ions and electrons in solution can be explained using the same physical phenomenon, namely, the Born self-energy (equation (S2)), and (c) the value assumed for the electron radius (equation (1)) does not conflict with experimental measurements and QED theory for the electron magnetic moment.

m
is the bare or Dirac mass that arises in the Dirac equation and , the Born self-energy term and the Coulomb interaction cancel in equation (S5), and consequently terms, as occurs for other ions, where Born e U can alternatively be viewed as arising from the work done against the Coulomb force in separating the electron and positron from e R to infinity.Thus, the (non-local) energy is conserved in the eBse model.In earlier publications [10,11] we have shown how Born e U quantitatively describes DE, within error bars, with no free parameters.

B
 would only disagree at the 15 th decimal place for this particular value of e R ) and the effects of this finite-sized electron radius are hidden within the error bars contained within equation (S3).